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- YU-MING CHU, CHENG ZONG, GEN-DI WANG, M. K. WANG
- 2011

We find the greatest value α and the least value β such that the double inequality αT (a,b) + (1 − α)G(a,b) < A(a,b) < β T (a,b) + (1 − β)G(a,b) holds for all a,b > 0 with a = b. Here T (a,b) , G(a,b) , and A(a,b) denote the Seiffert, geometric, and arithmetic means of two positive numbers a and b , respectively. An optimal double inequality between… (More)

In this paper, we establish a new double inequality between the Seiffert and harmonic means. The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal.

In this paper, we find the largest value α and least value β such that the double inequality L α (a,b) < M(a,b) < L β (a,b) holds for all a,b > 0 with a = b. Here, M(a,b) and L p (a,b) are the Neuman-Sándor and p-th generalized logarithmic means of a and b , respectively. Optimal combinations bounds of root-square and arithmetic means for Toader mean, An… (More)

In this paper, we find the greatest value α and the least values β , p , q and r in (0,1/2) such that the inequalities L(αa + (1 − α)b,αb + (1 − α)a) < P(a,b) < L(β a + (1 − β)b,β b + (1 − β)a) , H(pa + (1 − p)b, pb + (1 − p)a) > G(a,b) , H(qa + (1 − q)b,qb + (1 − q)a) > L(a,b) , and G(ra + (1 − r)b,rb + (1 − r)a) > L(a,b) hold for all a,b > 0 with a = b.… (More)